The party is seeking re-election following the resignation of Alexis Tsipras (photo) on the 21st of August.
Tsipras stepped down as Prime Minister, saying he had a "political and ethical responsibility" to allow the electorate to judge his administration’s work after it failed to live up to Syriza’s promise to end austerity.
Rather than renegotiate the harsh economic measures imposed by Greece’s international creditors, Tsipras ended up agreeing to the privatisation of much of the public sector and other reforms in exchange for a third massive bailout loan of €86bn (£62bn).
A poll in the leftist newspaper Efimerida ton Syntakton gave Syriza a slim 3.5 point lead over the conservative party New Democracy.
The survey, conducted by ProRata, said 23 per cent of voters would support Syriza, while 19.5 per cent would vote for New Democracy.
A previous ProRata poll in July showed a wider gap in Syriza’s favour, putting the party at 26 per cent compared to 15 per cent for New Democracy.
Popular Unity, the party of ex-Syriza dissidents, were supported by 3.5 per cent of voters. A party must win at least 3 per cent of the vote to enter the Greek Parliament.
Just over a quarter of those polled said they were undecided, making them the largest bloc.
Tsipras said he needed a stronger mandate to implement tough austerity measures.